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Nutka1998 [239]
3 years ago
5

Solve 10e^2x - 5 =23^x for x.

Mathematics
2 answers:
yawa3891 [41]3 years ago
5 0

10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}

bixtya [17]3 years ago
5 0

Answer:

B is the correct option choice !


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alekssr [168]

Answer:

s>3

Step-by-step explanation:

Step 1: Flip the equation.

-4/3s <-4

Step 2: Multiply both sides by 3/(-4).

(3/-4) x (-4/3s) < (3/-4) x (-4)

s > 3

7 0
3 years ago
An item is priced at $13.42. If the sales tax is 4%, what does the item cost including sales tax? If necessary, round to the nea
stiv31 [10]

Answer:

Total cost = $13.96

Step-by-step explanation:

The total to be paid for the item is the addition of its price plus the taxes. That is:

Total\,\,cost=13.42+0.04\,*\,13.42\\Total\,\,cost=13.42+0.5368\\Total\,\,cost==13.9568

Which can be rounded to $13.96

8 0
3 years ago
Tom's stockbroker offers an investment that is compounded continuously at an annual interest rate of 3.7%. If Tom wants a return
Anettt [7]

Answer:

It'll take 38.3 years to obtain the desired return of $25,000.

Step-by-step explanation:

In order to solve a continuosly coumponded interest question we need to apply the correct formula that is given bellow:

M = C*e^(r*t)

Where M is the final value, C is the initial value, r is the interest rate and t is the time at which the money was applied. Since he wants an return of $25,000 his final value must be the sum of the initial value with the desired return. So we have:

(25000 + 8000) = 8000*e^(0.037*t)

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e^(0.037*t) = 33000/8000

e^(0.037*t) = 4.125

ln[e^(0.037*t)] = ln(4.125)

t = ln(4.125)/(0.037)

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7 0
3 years ago
Caroline babysat for two families - the Nelsons and the Smiths. Use the info below to compare her earnings.
algol13

Answer:

She earns $6.50 from the Smiths which is 25 cents more than she earns at the Nelsons.

Step-by-step explanation:

To solve this problem you must find the hourly rate she earns at the Smiths.  This will allow you to compare to the hourly rate that is given for the Nelsons.  To find the Smiths hourly rate divide $39 by the 6 hours she babysat there.  This will have the hourly rate.  39/6=6.5.  This means she earns $6.50 an hour for the Smiths.  When comparing the rates it is clear that she earned 25 cents more at the Smiths.

7 0
3 years ago
10+ 40 % 5 x 2 <br> what’s the answer?
LuckyWell [14K]

Answer:

I'm going to assume that was supposed to be a division sign.. so 26.

Step-by-step explanation:

multiplication/division first

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then addition

16+10=26

4 0
3 years ago
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